Separation of variables in Einstein spaces. I. Two ignorable and one null coordinate
- 1 July 1981
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 14 (7) , 1675-1684
- https://doi.org/10.1088/0305-4470/14/7/023
Abstract
Computes and classifies all Einstein spaces and their corresponding coordinate systems such that the Hamilton-Jacobi equation admits a separation of variables with two ignorable and one essential null coordinates. The authors find that all such spaces correspond to plane-fronted gravitational waves of Petrov type N. They also give necessary conditions which a general space-time must have in order to admit coordinates of the type studied. Furthermore, the integrability conditions for Helmholtz (Schrodinger) separability are completely solved.Keywords
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